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Combined Rates questions can be daunting for anyone taking the GMAT.

Let’s take a look at this sample question and detailed solution.  Challenge yourself by trying out the problem first before reviewing the solution.

Car X began traveling at an average speed of 35 miles per hour.  After 72 minutes, car Y began traveling at an average speed of 49 miles per hour.  When both cars had traveled the same distance, both cars stopped.  How many miles did car X travel from the time car Y began traveling until both cars stopped?

(A) 105
(B) 120
(C) 140
(D) 147
(E) 168

Solution:

Step 1 is to determine how far car X traveled during the 72 minutes before car Y has started.  To do this, we first convert 72 minutes to 6/5 of an hour (that’s 72/60 simplified), in order to make sure our units match, as our speed is given in miles per hour.  Since rate * time = distance, we know that car X traveled 35mph * 6/5 hours = 42 miles.

Step 2 we need to determine a relative rate. We do this in order to figure out how many miles car Y gains on car X each hour.  To calculate this, subtract the rate of car X from the rate of car Y.  49mph – 35mph = 14mph, which is our relative rate in miles per hour, or the rate that Y gains on X per hour.

Step 3 take the distance car Y must gain on car X (that’s 42 miles, from step 1) and divide it by the number of miles car Y gains on X in an hour (that’s 14 mph from step 2) in order to find the number of hours it will take for both cars to travel the same distance: 42mi/14mph = 3 hours.

Finally, we are asked to find how far car X traveled after car Y starts.  We use the time we calculated from step 3, which is 3 hours, and multiply it by car X’s rate (35mph).  This gives us 3hrs * 35mph = 105 miles, which is choice (A) and the correct answer to this problem.